Bring a large pot of water to a boil. Add the noodles and cook as the label directs. Drain and rinse well under cold water; set aside.
Meanwhile, combine the mushroom broth, mirin, soy sauce and fish sauce in a medium skillet. Bring to a boil, then reduce the heat to a bare simmer. Season the salmon with salt and pepper and add to the skillet along with the bell pepper and celery. Cover and cook, carefully flipping once, until the salmon is cooked through and flakes at the touch, 21/2 to 3 minutes per side. Remove the salmon using a slotted spoon or fish spatula; discard the skin.
Return the broth mixture to a boil, then remove from the heat. Season with salt. Divide the noodles and basil among bowls. Ladle vegetables and broth into each bowl, top with the salmon and sprinkle with the sesame seeds.